The belay team has some real work on their hands.  For one thing, they are pulling two persons instead of one.  Get a second person to help the belay person by holding them down.  Have another person grab the taught line and walk down the line performing a vector pull.  This will ease the load on the belay team and pull the rescuer and swimmer to shore much faster.  It also provides an extra person closer to the landing zone for assistance.

Once you have the victim, cradle them in front of you and grab their PFD.  Another great approach is to slide one arm under the shoulder strap and grab the other shoulder strap.  You can still escape quickly if necessary and this leaves a free hand for grabbing a throw line or swimming.  If you are securely attached on your rescue tether, you can hold the victim facing away from you in a great big bear hug if they are not too large in diameter.  Another approach is to simply cross their chest with one arm (like a running back holds a football).  This leaves the other arm free to swim with or grab a throw line.

Talking to the victim in a clear and calm voice can improve the victim's confidence and avoid panic.  Let the victim know what you want them to do so they can help you.  If you are not in the right position (preferably upstream behind them), ask them to wait while you move into position.  If they are panicking, ask them to back off while you take evasive action.